or the following Geman-Yang model [1]}, [2]}: \( \inf _{u \in X, l \in Y}L_{GY}(u, l )\) , \(l =(l_1,l_2)^T\)  with \(L_{GY}(u , l )\)  defined by,
\(D(u) + \frac{\mu }{2} \Vert \nabla u -l \Vert _2^2 + \mu \int _{\Omega }H(l ;\frac{\lambda }{\mu }) \mathrm {d}\sigma , \ H(l ;\frac{\lambda }{\mu }): ={\left\lbrace \begin{array}{ll}\sqrt{\frac{\lambda }{\mu }} |l | -\frac{|l |^2}{2}, \ |l | \le \sqrt{\frac{\lambda }{\mu }}, \\\frac{\lambda }{2\mu }, \ \quad |l | > \sqrt{\frac{\lambda }{\mu }}.\end{array}\right.}\) 
